So the sound level is the only possible difference in sound between rooms?
Of course not. Read what I actually said which is “it often helps”.
Mainly the sound meter is a useful tool to identify differences in bass extension and levels Room to room. I’ve found some rooms are bass heavy and others bass shy and others just right. It helps to verify what you hear.
Bass levels have a big impact on what you hear. Too much bass tend to obscure detail in the midrange. Too little tends to make the midrange sound more pronounced.
The meter also helps confirm what you are hearing room to room and better understand why things sound different or not.
Also my ears are older and no longer hear “air” fully well out to 20khz, but the sound meter app on my iPhone has that covered much better than I. Just because I can’t hear something doesn’t mean a “high end” system gets a free pass to slack off.